相关论文: A systematic approach to reduced GLT
We study the homogenization problem of semi linear reflected partial differential equations (reflected PDEs for short) with nonlinear Neumann conditions. The non-linear term is a function of the solution but not of its gradient. The proof…
We apply a novel spectral graph technique, that of locally-biased semi-supervised eigenvectors, to study the diversity of galaxies. This technique permits us to characterize empirically the natural variations in observed spectra data, and…
Semi-supervised learning (SSL) has recently received increased attention from machine learning researchers. By enabling effective propagation of known labels in graph-based deep learning (GDL) algorithms, SSL is poised to become an…
We derive semiclassical expressions for spectra, weighted by matrix elements of a Gaussian observable, relevant to a range of molecular and mesoscopic systems. We apply the formalism to the particular example of the resonant tunneling diode…
We give a brief overview on the theory and phenomenology of generalized parton distributions (GPDs), including the recently developed framework of single-diffractive hard exclusive process for matching GPDs to experimental observables. We…
Utilizing machine learning to address partial differential equations (PDEs) presents significant challenges due to the diversity of spatial domains and their corresponding state configurations, which complicates the task of encompassing all…
Deep networks trained on the source domain show degraded performance when tested on unseen target domain data. To enhance the model's generalization ability, most existing domain generalization methods learn domain invariant features by…
The problem of labeled graph generation is gaining attention in the Deep Learning community. The task is challenging due to the sparse and discrete nature of graph spaces. Several approaches have been proposed in the literature, most of…
This thesis addresses two persistent and closely related challenges in modern deep learning, reliability and efficiency, through a unified framework grounded in Spectral Geometry and Random Matrix Theory (RMT). As deep networks and large…
Starting from the definition of an $n\times n$ $g$-Toeplitz matrix, $T_{n,g}(u)=\left[\widehat{u}_{r-gs}\right]_{r,s=0}^{n-1},$ where $g$ is a given nonnegative parameter, $\{\widehat{u}_{k}\}$ is the sequence of Fourier coefficients of the…
We summarize recent developments in understanding the concept of generalized parton distributions (GPDs), its relation to nucleon structure, and its application to high-Q2 electroproduction processes. Following a brief review of QCD…
Graph embedding seeks to build a low-dimensional representation of a graph G. This low-dimensional representation is then used for various downstream tasks. One popular approach is Laplacian Eigenmaps, which constructs a graph embedding…
Partial differential equations (PDEs) involving high contrast and oscillating coefficients are common in scientific and industrial applications. Numerical approximation of these PDEs is a challenging task that can be addressed, for example,…
In this paper, we perform the convergence analysis of unsupervised Legendre--Galerkin neural networks (ULGNet), a deep-learning-based numerical method for solving partial differential equations (PDEs). Unlike existing deep learning-based…
We present a discretization of the linear advection of differential forms on bounded domains. The framework previously established is extended to incorporate the Lie derivative, $\mathcal L$, by means of Cartan's homotopy formula. The…
Deep learning has significantly advanced building segmentation in remote sensing, yet models struggle to generalize on data of diverse geographic regions due to variations in city layouts and the distribution of building types, sizes and…
In the past years, we have been developing a novel technique, called Four-Dimensional Unsubtraction (FDU) which aims to obtain purely four-dimensional representations of the matrix elements contributing to physical observables. In this…
A discretization of a continuum theory with constraints or conserved quantities is called mimetic if it mirrors the conserved laws or constraints of the continuum theory at the discrete level. Such discretizations have been found useful in…
A generalized finite element method is proposed for solving a heterogeneous reaction-diffusion equation with a singular perturbation parameter $\varepsilon$, based on locally approximating the solution on each subdomain by solution of a…
We consider spatial discretizations by the finite section method of the restricted group algebra of a finitely generated discrete group, which is represented as a concrete operator algebra via its left-regular representation. Special…